Asymptotic expansions in time for rotating incompressible viscous fluids

We study the three-dimensional Navier-Stokes equations of rotating incompressible viscous fluids with periodic boundary conditions. The asymptotic expansions, as time goes to infinity, are derived in all Gevrey spaces for any Leray-Hopf weak solutions in terms of oscillating, exponentially decaying functions. The results are established for all non-zero rotation speeds, and for both cases with and without the zero spatial average of the solutions. Our method makes use of the Poincare waves to rewrite the equations, and then implements the Gevrey norm techniques to deal with the resulting time-dependent bi-linear form. Special solutions are also found which form infinite dimensional invariant linear manifolds. (C) 2020 L'Association Publications de l'Institut Henri Poincare. Published by Elsevier B.V. All rights reserved.

Automated summary

In this study, the three-dimensional Navier-Stokes equations for rotating incompressible viscous fluids with periodic boundary conditions are investigated. Asymptotic expansions in all Gevrey spaces are derived for Leray-Hopf weak solutions, using oscillating, exponentially decaying functions. The results are applicable for all non-zero rotation speeds, with and without zero spatial average of the solutions.